The square root of the number 96 is a number whose product with itself gives 96. The square root of a number can be positive or negative, real or imaginary. Now we will calculate the square root of 96 using various methods and a few interesting facts and problems as well.

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Square root of 96: √96 = 9.79796Square of 96: (96)2 = 9216 
1.What Is the Square Root of 96?
2.Is Square Root of 96 Rational or Irrational?
3.How to Find the Square Root of 96?
4.FAQs on Square Root of 96
5.Important Notes on Square Root of 96

What Is the Square Root of 96?


The square root of 96 is written as √96 = 9.79796The square root of 96 can also be written as 4√6 in simplified form.The square root of number 96 is not an integer so, it is not a perfect square.

Is the Square Root of 96 Rational or Irrational?


A number is known as a rational if it can be written in the form of p/q where q ≠ 0.The square root of 96 is a non-repeating and non-terminating number.So, the square root of 96 is an irrational number.


How to Find the Square Root of 96?


We will now find the square root of 96 using the following methods.

Square Root of 96 Using Prime Factorization Method

Prime factors of 96 in pairs: (2 × 2) × (2 × 2) × 2 × 3Square of 96 is √96: √ ((2 × 2)2 × 6)√96 = ±4√6

Square Root of 96 by Long Division

We will now find the square root of 96 by the long division method.

Start grouping the digits from the unit’s place in pairs of two digits by putting a bar/line on top of them. We have pair in this case (96).Find a number (a) such that a × a ≤ 96. So, a will be 9 as 9 × 9 = 81.Put a decimal in the quotient and dividend part simultaneously. Also, put 3 pairs of zero in the dividend part after the decimal.Bring down one pair of zero. Now our new dividend is 1500. Now find a number (b) such that 18b × b ≤ 1500. The number m will be 7 as 187 × 7 = 1309 ≤ 1500.Repeat the above step for the remaining two pairs of zeros.

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So, we get the square root of √96 = 9.797 by the long division method.

Explore square roots using illustrations and interactive examples.


Important Notes:


The square root of 96 is an irrational number.The square root of -96 is an imaginary number.The number 96 is not a perfect square.

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Challenging Questions


Find the value of √√96.Find the square root of all the factors of 96 except 1 and 96.